Question 312: Work, Energy and Power & Circular Motion

Question

In non-uniform circular motion, the ratio of tangential to radial acceleration is ($$r=$$ radius, $$\alpha=$$ angular acceleration and $$v=$$ linear velocity)

Accepted Answer

In non-uniform circular motion, two types of acceleration components are present: the tangential acceleration (which is responsible for the change in the speed of the particle moving along the circular path) and the radial (or centripetal) acceleration (which is responsible for the change in direction of the velocity of the particle). The tangential acceleration, $$a_t$$, is given by $$a_t = r \alpha$$, where $$\alpha$$ is the angular acceleration, and $$r$$ is the radius of the circle. The radial (centripetal) acceleration, $$a_r$$, is given by $$a_r = \frac{v^2}{r}$$, where $$v$$ is the linear (tangential) velocity of the particle.
The question asks for the ratio of tangential to radial acceleration, which is:
$$
\frac{a_t}{a_r} = \frac{r \alpha}{\frac{v^2}{r}} = \frac{r^2 \alpha}{v^2}
$$
Therefore, the correct option is:
Option D: $$\frac{r^2 \alpha}{v^2}$$

Answer

$$\frac{r \alpha}{v}$$

Answer

$$\frac{v^2}{r a}$$

Answer

$$\frac{r \alpha^2}{v^2}$$

Answer

$$\frac{r^2 \alpha}{v^2}$$

Work, Energy and Power & Circular Motion

In non-uniform circular motion, the ratio of tangential to radial acceleration is ($r= radius, \alpha= angular acceleration and v=$ linear velocity)

Choose the correct answer: